Achieving inverse shadows?
You can actually input values greater than one to color inputs of any shader. What that would mean is that the shader would reflect or transmit more light than it receives, which is obviously impossible in reality and in normal circumstances should not be used for realistic materials, however it is possible. You can also use Light Paths node to separately control how different kinds of calculated light rays are being rendered. So, it turns out you can chose to display a material as solid only to the camera while to the rest of the scene it can be transparent and have greater than 1 values for the light it transmits producing your desired effect: